A ball of mass m rolls down a movable wedge of mass M The an

A ball of mass m rolls down a movable wedge of mass M. The angle of the

wedge is , and it is free to slide on a smooth horizontal surface. The contact between the ball and the wedge

is perfect rough. Find the acceleration of the wedge.

mass of the ball is m

mass of wedge is M

the accelration of wedge, a = net force /effective mass

a = (m * g * sin(theta)/(I/r^2 + M))

and

moment of inertia of ball , I = (0.4 * m * r^2)

so,

a = (m * g * sin(theta)/((0.4 * m ) + M))

a = (m * g * sin(theta)/(0.4 * m + M)

the accelration of the wedge is (m * g * sin(theta)/(0.4 * m + M)